Negative Dependence, Scrambled Nets, and Variance Bounds

Published Online:https://doi.org/10.1287/moor.2017.0861

References

  • Aistleitner C, Dick J (2015) Functions of bounded variation, signed measures, and a general Koksma–Hlawka inequality. Acta Arithmetica 167(2):143–171.CrossrefGoogle Scholar
  • Beare B (2009) A generalization of Hoeffding’s lemma, and a new class of covariance inequalities. Statist. Probab. Lett. 79(5):637–642.CrossrefGoogle Scholar
  • Caflisch RE, Morokoff W, Owen AB (1997) Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance 1(1):27–46.CrossrefGoogle Scholar
  • Dick J, Pillichshammer F (2010) Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Dick J, Kuo FY, Sloan IH (2013) High-dimensional integration: The quasi-Monte Carlo way. Acta Numerica 22:133–288.CrossrefGoogle Scholar
  • Dunford N, Schwartz J (1957) Linear Operators, Part 1: General Theory (John Wiley & Sons, New York).Google Scholar
  • Faure H (1982) Discrépance des suites associées à un système de numération (en dimension s). Acta Arithmetica 41(4):337–351.CrossrefGoogle Scholar
  • Fréchet M (1910) Extension au cas des intégrales multiples d’une définition de l’intégrale due à Stieltjes. Nouvelles annales de mathématiques, 4è série 10:241–256.Google Scholar
  • Hammersley JM, Handscomb DC (1956) A new Monte Carlo technique: Antithetic variates. Proc. Cambridge Philosophical Soc. 52(3):449–475.CrossrefGoogle Scholar
  • Hickernell FJ (1998) Lattice rules: How well do they measure up? Hellekalek P, Larcher G, eds. Random and Quasi-Random Point Sets, Lecture Notes in Statistics, Vol. 138 (Springer, New York), 109–166.CrossrefGoogle Scholar
  • Hoeffding W (1940) Maßstabinvariante Korrelationstheorie. Schriften Math. Inst. Univ. Berlin 5:181–233.Google Scholar
  • Lehmann EL (1966) Some concepts of dependence. Ann. Math. Statist. 37(5):1137–1153.CrossrefGoogle Scholar
  • Mardia K, Thompson J (1972) Unified treatment of moment-formulae. Sankhya Ser. A 34(2):121–132.Google Scholar
  • Matoušek J (1998) On the L2-discrepancy for anchored boxes. J. Complexity 14(4):527–556.CrossrefGoogle Scholar
  • Mckay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245.Google Scholar
  • Nelsen R (2006) An Introduction to Copulas, Springer Series in Statistics, 2nd ed. (Springer, New York).Google Scholar
  • Niederreiter H (1992) Random Number Generation and Quasi-Monte Carlo Methods, SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 63 (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Owen AB (1997) Monte Carlo variance of scrambled equidistribution quadrature. SIAM J. Numerical Anal. 34(5):1884–1910.CrossrefGoogle Scholar
  • Owen AB (1998) Scrambling Sobol and Niederreiter-Xing points. J. Complexity 14(4):466–489.CrossrefGoogle Scholar
  • Owen AB (2003) Variance and discrepancy with alternative scramblings. ACM Trans. Modeling Comput. Simulation 13:363–378.CrossrefGoogle Scholar
  • Owen AB (2005) Multidimensional variation for quasi-Monte Carlo. Fan J, Li G, eds. Internat. Conf. Statist. Honour of Professor Kai-Tai Fang’s 65th Birthday (World Scientific Publishing, Singapore), 49–74.CrossrefGoogle Scholar
  • Prakasa Rao B (1998) Hoeffding identity, multivariance and multicorrelation. Statistics 32(1):13–29.CrossrefGoogle Scholar
  • Quesada-Molina J (1992) A generalization of an identity of Hoeffding and some applications. J. Ital. Statist. Soc. 1(3):405–411.CrossrefGoogle Scholar
  • Royden H (1968) Real Analysis, 2nd ed. (Macmillan, New York).Google Scholar
  • Sobol’ IM (1967) On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7(4):86–112.CrossrefGoogle Scholar
  • Sobol’ IM (1969) Multidimensional Quadrature Formulas and Haar Functions (Nauka, Moskow). In Russian.Google Scholar
  • Sobol’ IM (1993) Sensitivity estimates for nonlinear mathematical models. Math. Modeling Comput. Experiments 1:407–414. Published in Russian in 1990.Google Scholar
  • Tao T (2011) An Introduction to Measure Theory, Graduate Texts in Mathematics, Vol. 126 (Springer, New York).CrossrefGoogle Scholar
  • Wang R, Wang B (2015) Extreme negative dependence and risk aggregation. J. Multivariate Anal. 136:12–25.CrossrefGoogle Scholar
  • Young W (1917) On multiple integration by parts and the second theorem of the mean. Proc. London Math. Soc., Ser. 2 16:273–293.CrossrefGoogle Scholar
  • Zaremba S (1968) Some applications of multidimensional integration by parts. Ann. Poln. Math. 21(1):85–96.CrossrefGoogle Scholar
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